ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of LaH3 (Materials Project id mp-1018144)

        96       91       91        0        0        0  
        91       96       91        0        0        0  
        91       91       96        0        0        0  
         0        0        0       80        0        0  
         0        0        0        0       80        0  
         0        0        0        0        0       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92.667 GPaEV = 124.97 GPaGV = 49 GPaνV = 0.27523
ReussKR = 92.667 GPaER = 17.534 GPaGR = 5.9701 GPaνR = 0.46846
HillKH = 92.667 GPaEH = 75.037 GPaGH = 27.485 GPaνH = 0.36504

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 80 GPa 80 GPa 80 GPa 278 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.4332 GPa 186.37 GPa 3.5971 TPa–1 3.5971 TPa–1 2.5 GPa 80 GPa-1.1471.8781Value
Anisotropy 25.07 1.0000 32Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
-0.6372
0.6372
-0.4336
-0.6544
0.6544
0.3788
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
-0.7071
0.0000
-0.2682
0.2676
-0.9255
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane